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Notes on Number Theory and Discrete Mathematics, 2022 Corrigendum to “On the dimension of an Abelian group” [Notes on Number Theory and Discrete Mathematics, 2021, Volume 27, Number 4, Pages 267—275]
T. Tossavainen, P. Haukkanen
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Smooth affine group schemes over the dual numbers [PDF]
Épijournal de Géométrie Algébrique, 2019 We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 \to \text{Lie}(G, I) \to E \to G \to 1$ where G is an affine, smooth group ...
Matthieu ROMAGNY, Dajano Tossici
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Periodic balanced binary triangles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$.
Jonathan Chappelon
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Fractal projections with an application in number theory [PDF]
Ergodic Theory and Dynamical Systems, 2020 In this paper, we discuss a connection between geometric measure theory and number theory. This method brings a new point of view for some number-theoretic problems concerning digit expansions.
Han Yu
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On certain sums of number theory [PDF]
International Journal of Number Theory, 2020 We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions.
O. Bordellès
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Torsion primes for elliptic curves over degree 8 number fields [PDF]
Research in Number Theory, 2023 Let d≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\ge 1$$\end ...
Maleeha Khawaja
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Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation [PDF]
Communications in Number Theory and Physics, 2020 We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a ...
Imma G'alvez-Carrillo +2 more
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, 2006 Combining the arguments developed in the works of D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yildirim [Preprint, 2005, arXiv: math.NT/506067] and Y. Motohashi [Number theory in progress – A.
Y. Motohashi, J. Pintz
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An Introduction to Probabilistic Number Theory, 2020 : Let K be a number field. Then we completely classify the preperiodic portraits of the maps f ( x ) = x d + c where c ∈ K is an algebraic integer and d ≫ K 0 . More precisely, we prove that, up to accounting for the natural action of d th roots of unity
Don Redmond
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On the λ-stability of p-class groups along cyclic p-towers of a number field [PDF]
International Journal of Number Theory, 2021 . Let k be a number field, p ≥ 2 a prime and S a set of tame or wild finite places of k . We call K/k a totally S -ramified cyclic p -tower if Gal( K/k ) ≃ Z /p N Z and if S 6 = ∅ is totally ramified. Using analogues of Chevalley’s formula (Gras, Proc. Math.
Georges Gras
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